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Massachusetts could be among the first states in the country to raise money for social services by offering investors the chance to earn profits on programs they establish.

The approach is known as “social impact bonds’’ or “pay for success.’’ It is based on the idea that if programs backed by investors succeed in reducing, for example, the number of inmates in prison or the homeless population, governments will realize big savings, which they can tap to pay off investors with healthy returns. If the programs fail, the government would owe little or nothing.

The administration of Governor Deval Patrick is already sifting through more than two dozen suggestions from nonprofits on how to create such performance-based programs.

“We have a new fiscal reality in state government,’’ said Jay Gonzalez, the Massachusetts secretary of administration and finance. “We have to find a way to become more effective.’’

An example of those interested include Roca Inc., a Chelsea nonprofit that works with high-risk young adults. It has proposed an intervention program that would work with an estimated 650 young offenders and cost about $11 million over four years. But Roca estimated the program would save $25 million to $38 million in prison costs during that span by reducing the incarceration rate.

A model for social impact bonds is being tested in the United Kingdom, where the government has pledged to cut budget deficits and is experimenting with novel ways to raise money for social programs.

Faced with the costly problem of petty criminals returning to prison again and again, and unable to spend more on intervention programs that have produced only mixed results, the government last year turned to so-called social impact bonds.

It struck a deal with a nonprofit partnership to create an $8 million program to work with 3,000 inmates over six years at a prison in Peterborough, England, 75 miles north of London. Social Finance Ltd., which helps arrange financing for nonprofits, raised the money from 17 investors, mainly charitable foundations.

If the nonprofits succeed in cutting recidivism by 7.5 percent, the investors will get all their money back. If they reduce the rate further, investors could receive up to $12.8 million, a nearly 60 percent profit.

If the effort fails to reduce recidivism by at least 7.5 percent, the government won’t owe investors anything.

“We can no longer fund everything,’’ said Hugo Biggs, a press officer for the British Ministry of Justice. “So going forward, we are going to pay for what works.’’

Here in the United States, federal, state, and local officials are considering similar experiments to tie government funding to results. President Obama, for example, earmarked $100 million in his 2012 budget for a performance-based initiative called “pay for success.’’ New York City and several other states, including Pennsylvania and North Carolina, have expressed interest in the experiment.

Boston is expected to play a critical role in developing new approaches to financing social services. Two nonprofits working to create social impact bonds are based in Boston: Social Finance Inc., the sister organization to the one behind the United Kingdom experiment, and Third Sector Capital Partners, a nonprofit investment bank. Both organizations are in discussions with Massachusetts and other states.

George Overholser, a former venture capitalist who cofounded Third Sector, said the potential for performance-based models has exploded in recent years because governments have developed more sophisticated databases and tracking systems, making it easier to follow prisoners, homeless people, and others touched by government programs over long periods of time.

“The government data is finally in good enough shape that we can be more scientific in assessing the true impact,’’ Overholser said. “Before it was too unreliable. The data was all over the place.’’

Overholser said philanthropists and foundations will probably be the first to show interest in funding social impact bonds. But if they prove successful, he said, traditional investors, such as pension funds, could provide money as well.

To be sure, Overholser said, private investors will play only a small role in funding the nation’s social programs. But he said these new mechanisms could demonstrate powerful ways to save money or improve services, which could then be replicated. “This is not about replacing government funding with private financing,’’ Overholser said. “This is about creating a feedback loop. It’s about shining a light on where investments could best be made.’’

Performance-based initiatives still may face complications. Government agencies and nonprofits could have trouble agreeing on performance measures, for instance. And it is unclear whether the approach would work for every type of social service program.

“It’s good to try new things,’’ said Joe Kriesberg, chief executive of the Massachusetts Association of Community Development Corporations. “But it doesn’t solve all the challenges and problems we have in funding serious social ills.’’